Knowable moments for high-order stochastic characterization and modelling of hydrological processes

D. Koutsoyiannis, Knowable moments for high-order stochastic characterization and modelling of hydrological processes, Hydrological Sciences Journal, 64 (1), 19–33, doi:10.1080/02626667.2018.1556794, 2019.

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[English]

Classical moments, raw or central, express important theoretical properties of probability distributions but can hardly be estimated from typical hydrological samples for orders beyond two. L-moments are better estimated, but they all are of first order in terms of the process of interest; while they are effective in inferring the marginal distribution of stochastic processes, they cannot characterize even secondorder dependence of processes (autocovariance, climacogram, power spectrum) and thus they cannot help in stochastic modelling. Picking from both categories, we introduce knowable (K-) moments, which combine advantages of both classical and L-moments, and enable reliable estimation from samples and effective description of high-order statistics, useful for marginal and joint distributions of stochastic processes. Further, we extend recent stochastic tools by introducing the K-climacogram and the K-climacospectrum, which enable characterization, in terms of univariate functions, of high-order properties of stochastic processes, as well as preservation thereof in simulations.

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Our works referenced by this work:

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12. D. Koutsoyiannis, Generic and parsimonious stochastic modelling for hydrology and beyond, Hydrological Sciences Journal, 61 (2), 225–244, doi:10.1080/02626667.2015.1016950, 2016.
13. Y. Markonis, and D. Koutsoyiannis, Scale-dependence of persistence in precipitation records, Nature Climate Change, 6, 399–401, doi:10.1038/nclimate2894, 2016.
14. F. Lombardo, E. Volpi, D. Koutsoyiannis, and F. Serinaldi, A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall, Water Resources Research, 53 (6), 4586–4605, doi:10.1002/2017WR020529, 2017.
15. D. Koutsoyiannis, Entropy production in stochastics, Entropy, 19 (11), 581, doi:10.3390/e19110581, 2017.
16. T. Iliopoulou, S.M. Papalexiou, Y. Markonis, and D. Koutsoyiannis, Revisiting long-range dependence in annual precipitation, Journal of Hydrology, 556, 891–900, doi:10.1016/j.jhydrol.2016.04.015, 2018.
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18. D. Koutsoyiannis, P. Dimitriadis, F. Lombardo, and S. Stevens, From fractals to stochastics: Seeking theoretical consistency in analysis of geophysical data, Advances in Nonlinear Geosciences, edited by A.A. Tsonis, 237–278, doi:10.1007/978-3-319-58895-7_14, Springer, 2018.

Our works that reference this work:

1. D. Koutsoyiannis, Time’s arrow in stochastic characterization and simulation of atmospheric and hydrological processes, Hydrological Sciences Journal, doi:10.1080/02626667.2019.1600700, 2019.

Tagged under: Most recent works, Stochastics